Model help:TopoFlow-Infiltration-Richards 1D
TopoFlow-Infiltration-Richards 1D
This module is the infiltration process component (Richards 1D method) for a D8-based, spatial hydrologic model.
Model introduction
This process component is part of a spatially-distributed hydrologic model called TopoFlow, but it can now be used as a stand-alone model.
Model parameters
Uses ports
• Meteorology
• Snow (Snowmelt)
• Evap (Evaporation)
• Satzone (Subsurface flow in saturated zone)
• Channels (surface water flow in a network of channels)
Provides ports
• Infil (Infiltration)
• Configure (tabbed dialog GUI to change settings)
• Run (only if used as the Driver)
Main equations
- Darcy's law for vertical flow rate
[math]\displaystyle{ v= K \ast \left ( 1 - \Psi\right) }[/math] (1)
- Conservation of mass, with source/sink term J (subscripts are partial derivatives)
[math]\displaystyle{ v_{z}= J - \theta_{t} }[/math] (2)
- Effective saturation or scaled water content (in [0,1]. Equals 0 when θ = θ_{r}. Equals 1 when θ = θ_{s}.))
[math]\displaystyle{ \Theta_{e}= \left ( \theta - \theta_{r}\right) / \left ( \theta_{s} - \theta_{r} \right) }[/math] (3)
- Hydraulic conductivity
[math]\displaystyle{ K= K_{s} \ast \Theta_{e}^{\frac{\eta}{\lambda}} }[/math] (4)
- Pressure head
[math]\displaystyle{ \Psi= \Psi_{B} \left ( \Theta_{e}^{\frac{-c}{\lambda}} - 1 \right)^{\frac{1}{c}} - \Psi_{A} }[/math] (5)
Symbol | Description | Unit |
---|---|---|
K_{s} | saturated hydraulic conductivity | [m / s] |
K_{i} | initial hydraulic conductivity (typically much less than K_{s}) | [m / s] |
θ_{s} | soil water content at ψ = 0 (often set to the soil porosity, φ) | [-] |
θ_{i} | initial soil water content | [-] |
θ_{r} | residual soil water content (must be < θ_{i}) | [-] |
ψ_{B} | bubbling pressure head (also called air-entry pressure, ψ_{ae}) | m |
ψ_{A} | pressure head offset parameter | m |
λ | pore-size distribution parameter (alt. notation - 1/b) | - |
η | unit less, equals to 2 + ( 3*λ ) | |
c | transitional Brooks-Corey curvature parameter | |
dz_{nodes} | vertical distance between nodes | m |
n_{nodes} | number of subsurface vertical nodes | |
J | source / sink | |
θ_{t} | - | |
Θ_{e} | effective saturation or scaled water content (unitless in [0,1]) |
Output
Symbol | Description | Unit |
---|---|---|
θ | soil moisture | none |
ψ | pressure head | m |
K | hydraulic conductivity | m / s |
v | vertical flow rate | m / s |
Notes
Notes on Input Parameters
For each variable, you may choose from the droplist of data types. For the "Scalar" data type, enter a numeric value with the units indicated in the dialog. For the other data types, enter a filename. Values in files must also use the indicated units.
Single grids and grid sequences are assumed to be stored as RTG and RTS files, respectively. Time series are assumed to be stored as text files, with one value per line. For a time series or grid sequence, the time between values must coincide with the timestep provided.
The current version allows up to 3 different soil layers, each with its own soil properties and number of vertical nodes. The soil layer number is indicated at the top of the dialog and you use the Next and Back buttons to view settings for the various layers.
Notes on the Equations
All variables and their units can be seen by expanding the Nomenclature section above.
These equations are used to compute the time evolution of 1D (vertical, subsurface) profiles for (1) soil moisture, θ, (2) pressure head, ψ, (3) hydraulic conductivity, K and (4) vertical flow rate, v. TopoFlow solves these equations separately to get time-evolving profiles for every grid cell in a DEM. The result is a 3D grid for each of these four variables that spans the unsaturated zone. The third equation above just defines a variable that is used in the 4th and 5th equations, so the coupled set constitutes 4 equations to be solved for 4 unknowns. These equations can be combined into one nonlinear, parabolic, second-order PDE (partial differential equation) known as the one-dimensional Richards' equation.
The infiltration rate is simply the vertical flow rate at the ground surface, denoted by v_{0}.
Soil moisture is simply another term for the water content in the case where the porous medium is a soil.
Subscripts in the first two equations indicate partial derivatives with respect to the vertical coordinate, z. Note that z is the vertical distance below the ground surface, in meters.
More information on how soil is modeled in TopoFlow along with published soil property tables can be found on this soil properties page.
Two other, simpler methods for modeling infiltration are described on the help pages for the Green-Ampt method and the Smith-Parlange 3-parameter method.
Examples
An example run with input parameters, BLD files, as well as a figure / movie of the output
Follow the next steps to include images / movies of simulations:
- Upload file: https://csdms.colorado.edu/wiki/Special:Upload
- Create link to the file on your page: [[Image:<file name>]].
See also: Help:Images or Help:Movies
Developer(s)
References
Dingman, S.L. (2002) Physical Hydrology, 2nd ed., Prentice-Hall, Upper Saddle River, New Jersey, 646 pp.
Smith, R.E. (2002) Infiltration Theory for Hydrologic Applications, Water Resources Monograph 15, AGU, 212 pp.
Links
Related Help Pages
- Model help:TopoFlow-Infiltration-Green-Ampt
- Model help:TopoFlow-Infiltration-Smith-Parlange
- Model help:TopoFlow-Saturated_Zone-Darcy_Layers
- Model help:TopoFlow-Soil Properties Page
Model Metadata